Clinton, in the Middle East for a three-day visit, issued an unusually sharp rebuke to Bahrain, where security forces used tear gas and rubber-coated bullets earlier in the day to clear hundreds of demonstrators from the Bahraini capital's main square. Bahraini police were backed by personnel from four neighboring Persian Gulf states in clashes that reportedly left two demonstrators dead.

"They are on the wrong track," Clinton told reporters in Cairo. "There is no security answer to this, and the sooner they get back to the negotiating table and start trying to answer the legitimate needs of the people, the sooner there can be a resolution."

The violence in Bahrain and fighting in Libya overshadowed Clinton's first visit to the region since Egyptian President Hosni Mubarak quit his post in the face of massive protests in Cairo's Tahrir Square. Clinton paid tribute to Egypt's pro-democracy revolution with a surprise visit to the famous plaza, where she shook hands with ordinary Egyptians. Some greeted her enthusiastically while others watched with indifference or bemusement.

"Welcome to Egypt," some called out in English.

"Thank you for walking in Tahrir Square," said one middle-aged man.

Afterward, Clinton called the experience "thrilling."

"To see where this revolution happened and all that it has meant to the world is extraordinary for me," Clinton said as she walked. "It's just a great reminder of the power of the human spirit and universal desire for human rights and democracy."

Clinton spent much of the day consulting with Egyptian leaders and others on an international response to worsening violence in Libya and Bahrain, while also hearing from a wide range of Egyptians on how the United States can support the country's transitional government as it prepares for elections.

Clinton expressed dismay at the crackdown on protesters in Bahrain, saying the Obama administration has raised concerns with Bahrani leaders "at the highest level," and also with four other gulf countries that agreed to send security forces to the Sunni-led country.

"We find what's happening in Bahrain alarming," Clinton said. "We think that there is no security answer to the aspirations and demands of the demonstrators."

Clinton has been consulting with regional leaders on an international response to the fighting in Libya, as European allies push for new U.N. Security Council resolutions that could include authorization for a no-fly zone to shield Libyan rebels from assaults by Moammar Gaddafi's warplanes.